SUMMARYDroplet positions in atmospheric clouds are random but possibly correlated on some scales. This 'clustering' must be quanti ed in order to account for it in theories of cloud evolution and radiative transfer. Tools as varied as droplet concentration power spectrum, Fishing test, and fractal correlation analysis have been used to describe the small-scale nature of clouds, and it has been dif cult to compare conclusions systematically. Here we show, by using the correlation-uctuation theorem and the Wiener-Khinchin theorem, that all of these measures can be related to the pair-correlation function. It is argued that the pair-correlation function is ideal for quantifying droplet clustering because it contains no scale memory and because of its quantitative link to the Poisson process.
We study the dynamics of a repulsively coupled array of phase oscillators. For an array of globally coupled identical oscillators, repulsive coupling results in a family of synchronized regimes characterized by zero mean field. If the number of oscillators is sufficiently large, phase locking among oscillators is destroyed, independently of the coupling strength, when the oscillators' natural frequencies are not the same. In locally coupled networks, however, phase locking occurs even for nonidentical oscillators when the coupling strength is sufficiently strong.
The spatial clustering of drops is a defining characteristic of rain on all scales from centimeters to kilometers. It is the physical basis for much of the observed variability in rain. The authors report here on the temporal-spatial 1-min counts using a network of 21 optical disdrometers over a small area near Charleston, South Carolina. These observations reveal significant differences between spatial and temporal structures (i.e., clustering) for different sizes of drops, which suggest that temporal observations of clustering cannot be used to infer spatial clustering simply using by an advection velocity as has been done in past studies. It is also shown that both spatial and temporal clustering play a role in rain variability depending upon the drop size. The more convective rain is dominated by spatial clustering while the opposite holds for the more stratiform rain.Like previous time series measurements by a single disdrometer but in contradiction with widely accepted drop size distribution power-law relations, it is also shown that there is a linear relation between 1-min averages of the rainfall rate R over the network and the average total number of drops N t . However, the network (area) R-N t relation differs from those derived strictly from time series observations by individual disdrometers. These differences imply that the temporal and spatial size distributions and their variabilities are not equivalent.
The extent of droplet clustering in turbulent clouds has remained largely unquantified, and yet is of possible relevance to precipitation formation and radiative transfer. To that end, data gathered by an airborne holographic instrument are used to explore the three-dimensional spatial statistics of cloud droplet positions in homogeneous stratiform boundary-layer clouds. The three-dimensional radial distribution functions g(r) reveal unambiguous evidence of droplet clustering. Three key theoretical predictions are observed: existence of positive correlations, onset of correlation in the turbulence dissipation range, and monotonic increase of g(r) with decreasing r. This implies that current theory captures the essential processes contributing to clustering, even at large Reynolds numbers typical of the atmosphere.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.